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  Coupled pattern learner

  Coupled Pattern Learner (CPL) is a machine learning algorithm which couples the semi-supervised learning of categories and relations to forestall the problem of semantic drift associated with boot-strap learning methods. == Coupled Pattern Learner == Semi-supervised learning approaches using a small number of labeled examples with many unlabeled examples are usually unreliable as they produce an internally consistent, but incorrect set of extractions. CPL solves this problem by simultaneously learning classifiers for many different categories and relations in the presence of an ontology defining constraints that couple the training of these classifiers. It was introduced by Andrew Carlson, Justin Betteridge, Estevam R. Hruschka Jr. and Tom M. Mitchell in 2009. == CPL overview == CPL is an approach to semi-supervised learning that yields more accurate results by coupling the training of many information extractors. Basic idea behind CPL is that semi-supervised training of a single type of extractor such as ‘coach’ is much more difficult than simultaneously training many extractors that cover a variety of inter-related entity and relation types. Using prior knowledge about the relationships between these different entities and relations CPL makes unlabeled data as a useful constraint during training. For e.g., ‘coach(x)’ implies ‘person(x)’ and ‘not sport(x)’. == CPL description == === Coupling of predicates === CPL primarily relies on the notion of coupling the learning of multiple functions so as to constrain the semi-supervised learning problem. CPL constrains the learned function in two ways. Sharing among same-arity predicates according to logical relations Relation argument type-checking === Sharing among same-arity predicates === Each predicate P in the ontology has a list of other same-arity predicates with which P is mutually exclusive. If A is mutually exclusive with predicate B, A’s positive instances and patterns become negative instances and negative patterns for B. For example, if ‘city’, having an instance ‘Boston’ and a pattern ‘mayor of arg1’, is mutually exclusive with ‘scientist’, then ‘Boston’ and ‘mayor of arg1’ will become a negative instance and a negative pattern respectively for ‘scientist.’ Further, Some categories are declared to be a subset of another category. For e.g., ‘athlete’ is a subset of ‘person’. === Relation argument type-checking === This is a type checking information used to couple the learning of relations and categories. For example, the arguments of the ‘ceoOf’ relation are declared to be of the categories ‘person’ and ‘company’. CPL does not promote a pair of noun phrases as an instance of a relation unless the two noun phrases are classified as belonging to the correct argument types. === Algorithm description === Following is a quick summary of the CPL algorithm. Input: An ontology O, and a text corpus C Output: Trusted instances/patterns for each predicate for i=1,2,...,∞ do foreach predicate p in O do EXTRACT candidate instances/contextual patterns using recently promoted patterns/instances; FILTER candidates that violate coupling; RANK candidate instances/patterns; PROMOTE top candidates; end end ==== Inputs ==== A large corpus of Part-Of-Speech tagged sentences and an initial ontology with predefined categories, relations, mutually exclusive relationships between same-arity predicates, subset relationships between some categories, seed instances for all predicates, and seed patterns for the categories. ==== Candidate extraction ==== CPL finds new candidate instances by using newly promoted patterns to extract the noun phrases that co-occur with those patterns in the text corpus. CPL extracts, Category Instances Category Patterns Relation Instances Relation Patterns ==== Candidate filtering ==== Candidate instances and patterns are filtered to maintain high precision, and to avoid extremely specific patterns. An instance is only considered for assessment if it co-occurs with at least two promoted patterns in the text corpus, and if its co-occurrence count with all promoted patterns is at least three times greater than its co-occurrence count with negative patterns. ==== Candidate ranking ==== CPL ranks candidate instances using the number of promoted patterns that they co-occur with so that candidates that occur with more patterns are ranked higher. Patterns are ranked using an estimate of the precision of each pattern. ==== Candidate promotion ==== CPL ranks the candidates according to their assessment scores and promotes at most 100 instances and 5 patterns for each predicate. Instances and patterns are only promoted if they co-occur with at least two promoted patterns or instances, respectively. == Meta-Bootstrap Learner == Meta-Bootstrap Learner (MBL) was also proposed by the authors of CPL. Meta-Bootstrap learner couples the training of multiple extraction techniques with a multi-view constraint, which requires the extractors to agree. It makes addition of coupling constraints on top of existing extraction algorithms, while treating them as black boxes, feasible. MBL assumes that the errors made by different extraction techniques are independent. Following is a quick summary of MBL. Input: An ontology O, a set of extractors ε Output: Trusted instances for each predicate for i=1,2,...,∞ do foreach predicate p in O do foreach extractor e in ε do Extract new candidates for p using e with recently promoted instances; end FILTER candidates that violate mutual-exclusion or type-checking constraints; PROMOTE candidates that were extracted by all extractors; end end Subordinate algorithms used with MBL do not promote any instance on their own, they report the evidence about each candidate to MBL and MBL is responsible for promoting instances. == Applications == In their paper authors have presented results showing the potential of CPL to contribute new facts to existing repository of semantic knowledge, Freebase

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  ID3 algorithm

  In decision tree learning, ID3 (Iterative Dichotomiser 3) is a greedy algorithm invented by Ross Quinlan used to generate a decision tree from a dataset. ID3 is the precursor to the C4.5 algorithm. The 3 in the name is meant to signify that this was Quinlan's third attempt at a model based on entropy-based splitting, and the term dichotimser is a misnomer as it implies a binary split, but the ID3 algorithm can split on multi-valued attributes. == Algorithm == The ID3 algorithm begins with the original set S {\displaystyle S} as the root node. On each iteration of the algorithm, it iterates through every unused attribute of the set S {\displaystyle S} and calculates the entropy H ( S ) {\displaystyle \mathrm {H} {(S)}} or the information gain I G ( S ) {\displaystyle IG(S)} of that attribute. It then selects the attribute which has the smallest entropy (or largest information gain) value. The set S {\displaystyle S} is then split or partitioned by the selected attribute to produce subsets of the data. (For example, a node can be split into child nodes based upon the subsets of the population whose ages are less than 50, between 50 and 100, and greater than 100.) The algorithm continues to recurse on each subset, considering only attributes never selected before. Recursion on a subset may stop in one of these cases: every element in the subset belongs to the same class; in which case the node is turned into a leaf node and labelled with the class of the examples. there are no more attributes to be selected, but the examples still do not belong to the same class. In this case, the node is made a leaf node and labelled with the most common class of the examples in the subset. there are no examples in the subset, which happens when no example in the parent set was found to match a specific value of the selected attribute. An example could be the absence of a person among the population with age over 100 years. Then a leaf node is created and labelled with the most common class of the examples in the parent node's set. Throughout the algorithm, the decision tree is constructed with each non-terminal node (internal node) representing the selected attribute on which the data was split, and terminal nodes (leaf nodes) representing the class label of the final subset of this branch. === Summary === Calculate the entropy of every attribute a {\displaystyle a} of the data set S {\displaystyle S} . Partition ("split") the set S {\displaystyle S} into subsets using the attribute for which the resulting entropy after splitting is minimized; or, equivalently, information gain is maximum. Make a decision tree node containing that attribute. Recurse on subsets using the remaining attributes. === Properties === ID3 does not guarantee an optimal solution. It can converge upon local optima. It uses a greedy strategy by selecting the locally best attribute to split the dataset on each iteration. The algorithm's optimality can be improved by using backtracking during the search for the optimal decision tree at the cost of possibly taking longer. ID3 can overfit the training data. To avoid overfitting, smaller decision trees should be preferred over larger ones. This algorithm usually produces small trees, but it does not always produce the smallest possible decision tree. ID3 is harder to use on continuous data than on factored data (factored data has a discrete number of possible values, thus reducing the possible branch points). If the values of any given attribute are continuous, then there are many more places to split the data on this attribute, and searching for the best value to split by can be time-consuming. === Usage === The ID3 algorithm is used by training on a data set S {\displaystyle S} to produce a decision tree which is stored in memory. At runtime, this decision tree is used to classify new test cases (feature vectors) by traversing the decision tree using the features of the datum to arrive at a leaf node. == The ID3 metrics == === Entropy === Entropy H ( S ) {\displaystyle \mathrm {H} {(S)}} is a measure of the amount of uncertainty in the (data) set S {\displaystyle S} (i.e. entropy characterizes the (data) set S {\displaystyle S} ). H ( S ) = ∑ x ∈ X − p ( x ) log 2 ⁡ p ( x ) {\displaystyle \mathrm {H} {(S)}=\sum _{x\in X}{-p(x)\log _{2}p(x)}} Where, S {\displaystyle S} – The current dataset for which entropy is being calculated This changes at each step of the ID3 algorithm, either to a subset of the previous set in the case of splitting on an attribute or to a "sibling" partition of the parent in case the recursion terminated previously. X {\displaystyle X} – The set of classes in S {\displaystyle S} p ( x ) {\displaystyle p(x)} – The proportion of the number of elements in class x {\displaystyle x} to the number of elements in set S {\displaystyle S} When H ( S ) = 0 {\displaystyle \mathrm {H} {(S)}=0} , the set S {\displaystyle S} is perfectly classified (i.e. all elements in S {\displaystyle S} are of the same class). In ID3, entropy is calculated for each remaining attribute. The attribute with the smallest entropy is used to split the set S {\displaystyle S} on this iteration. Entropy in information theory measures how much information is expected to be gained upon measuring a random variable; as such, it can also be used to quantify the amount to which the distribution of the quantity's values is unknown. A constant quantity has zero entropy, as its distribution is perfectly known. In contrast, a uniformly distributed random variable (discretely or continuously uniform) maximizes entropy. Therefore, the greater the entropy at a node, the less information is known about the classification of data at this stage of the tree; and therefore, the greater the potential to improve the classification here. As such, ID3 is a greedy heuristic performing a best-first search for locally optimal entropy values. Its accuracy can be improved by preprocessing the data. === Information gain === Information gain I G ( A ) {\displaystyle IG(A)} is the measure of the difference in entropy from before to after the set S {\displaystyle S} is split on an attribute A {\displaystyle A} . In other words, how much uncertainty in S {\displaystyle S} was reduced after splitting set S {\displaystyle S} on attribute A {\displaystyle A} . I G ( S , A ) = H ( S ) − ∑ t ∈ T p ( t ) H ( t ) = H ( S ) − H ( S | A ) . {\displaystyle IG(S,A)=\mathrm {H} {(S)}-\sum _{t\in T}p(t)\mathrm {H} {(t)}=\mathrm {H} {(S)}-\mathrm {H} {(S|A)}.} Where, H ( S ) {\displaystyle \mathrm {H} (S)} – Entropy of set S {\displaystyle S} T {\displaystyle T} – The subsets created from splitting set S {\displaystyle S} by attribute A {\displaystyle A} such that S = ⋃ t ∈ T t {\displaystyle S=\bigcup _{t\in T}t} p ( t ) {\displaystyle p(t)} – The proportion of the number of elements in t {\displaystyle t} to the number of elements in set S {\displaystyle S} H ( t ) {\displaystyle \mathrm {H} (t)} – Entropy of subset t {\displaystyle t} In ID3, information gain can be calculated (instead of entropy) for each remaining attribute. The attribute with the largest information gain is used to split the set S {\displaystyle S} on this iteration.

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  Dispersive flies optimisation

  Dispersive flies optimisation (DFO) is a bare-bones swarm intelligence algorithm which is inspired by the swarming behaviour of flies hovering over food sources. DFO is a simple optimiser which works by iteratively trying to improve a candidate solution with regard to a numerical measure that is calculated by a fitness function. Each member of the population, a fly or an agent, holds a candidate solution whose suitability can be evaluated by their fitness value. Optimisation problems are often formulated as either minimisation or maximisation problems. DFO was introduced with the intention of analysing a simplified swarm intelligence algorithm with the fewest tunable parameters and components. In the first work on DFO, this algorithm was compared against a few other existing swarm intelligence techniques using error, efficiency and diversity measures. It is shown that despite the simplicity of the algorithm, which only uses agents’ position vectors at time t to generate the position vectors for time t + 1, it exhibits a competitive performance. Since its inception, DFO has been used in a variety of applications including medical imaging and image analysis as well as data mining and machine learning. == Algorithm == DFO bears many similarities with other existing continuous, population-based optimisers (e.g. particle swarm optimization and differential evolution). In that, the swarming behaviour of the individuals consists of two tightly connected mechanisms, one is the formation of the swarm and the other is its breaking or weakening. DFO works by facilitating the information exchange between the members of the population (the swarming flies). Each fly x {\displaystyle \mathbf {x} } represents a position in a d-dimensional search space: x = ( x 1 , x 2 , … , x d ) {\displaystyle \mathbf {x} =(x_{1},x_{2},\ldots ,x_{d})} , and the fitness of each fly is calculated by the fitness function f ( x ) {\displaystyle f(\mathbf {x} )} , which takes into account the flies' d dimensions: f ( x ) = f ( x 1 , x 2 , … , x d ) {\displaystyle f(\mathbf {x} )=f(x_{1},x_{2},\ldots ,x_{d})} . The pseudocode below represents one iteration of the algorithm: for i = 1 : N flies x i . fitness = f ( x i ) {\displaystyle \mathbf {x_{i}} .{\text{fitness}}=f(\mathbf {x} _{i})} end for i x s {\displaystyle \mathbf {x} _{s}} = arg min [ f ( x i ) ] , i ∈ { 1 , … , N } {\textstyle [f(\mathbf {x} _{i})],\;i\in \{1,\ldots ,N\}} for i = 1 : N and i ≠ s {\displaystyle i\neq s} for d = 1 : D dimensions if U ( 0 , 1 ) < Δ {\displaystyle U(0,1)<\Delta } x i d t + 1 = U ( x min , d , x max , d ) {\displaystyle x_{id}^{t+1}=U(x_{\min ,d},x_{\max ,d})} else x i d t + 1 = x i n d t + U ( 0 , 1 ) ( x s d t − x i d t ) {\displaystyle x_{id}^{t+1}=x_{i_{nd}}^{t}+U(0,1)(x_{sd}^{t}-x_{id}^{t})} end if end for d end for i In the algorithm above, x i d t + 1 {\displaystyle x_{id}^{t+1}} represents fly i {\displaystyle i} at dimension d {\displaystyle d} and time t + 1 {\displaystyle t+1} ; x i n d t {\displaystyle x_{i_{nd}}^{t}} presents x i {\displaystyle x_{i}} 's best neighbouring fly in ring topology (left or right, using flies indexes), at dimension d {\displaystyle d} and time t {\displaystyle t} ; and x s d t {\displaystyle x_{sd}^{t}} is the swarm's best fly. Using this update equation, the swarm's population update depends on each fly's best neighbour (which is used as the focus μ {\displaystyle \mu } , and the difference between the current fly and the best in swarm represents the spread of movement, σ {\displaystyle \sigma } ). Other than the population size N {\displaystyle N} , the only tunable parameter is the disturbance threshold Δ {\displaystyle \Delta } , which controls the dimension-wise restart in each fly vector. This mechanism is proposed to control the diversity of the swarm. Other notable minimalist swarm algorithm is Bare bones particle swarms (BB-PSO), which is based on particle swarm optimisation, along with bare bones differential evolution (BBDE) which is a hybrid of the bare bones particle swarm optimiser and differential evolution, aiming to reduce the number of parameters. Alhakbani in her PhD thesis covers many aspects of the algorithms including several DFO applications in feature selection as well as parameter tuning. == Applications == Some of the recent applications of DFO are listed below: Optimising support vector machine kernel to classify imbalanced data Quantifying symmetrical complexity in computational aesthetics Analysing computational autopoiesis and computational creativity Identifying calcifications in medical images Building non-identical organic structures for game's space development Deep Neuroevolution: Training Deep Neural Networks for False Alarm Detection in Intensive Care Units Identification of animation key points from 2D-medialness maps

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  Joseph Nechvatal

  Joseph Nechvatal (born January 15, 1951) is an American post-conceptual digital artist and art theoretician who creates computer-assisted paintings and computer animations, often using custom computer viruses. == Life and work == Joseph Nechvatal was born in Chicago. He studied fine art and philosophy at Southern Illinois University Carbondale, Cornell University, and Columbia University. He earned a Doctor of Philosophy in Philosophy of Art and Technology at the Planetary Collegium at University of Wales, Newport and has taught art theory and art history at the School of Visual Arts. He has had many solo exhibitions and is one of five artists that art historian Patrick Frank examines in his 2024 book Art of the 1980s: As If the Digital Mattered. His work in the late 1970s and early 1980s chiefly consisted of postminimal gray palimpsest-like drawings that were often photo-mechanically enlarged. Beginning in 1979 he became associated with the artist group Colab, organized the Public Arts International/Free Speech series, and helped established the non-profit group ABC No Rio. In 1983 he co-founded the avant-garde electronic art music audio project Tellus Audio Cassette Magazine. In 1984, Nechvatal began work on an opera called XS: The Opera Opus (1984-6) with the no wave musical composer Rhys Chatham. He began using computers and robotics to make post-conceptual paintings in 1986 and later, in his signature work, began to employ self-created computer viruses. From 1991 to 1993, he was artist-in-residence at the Louis Pasteur Atelier in Arbois, France and at the Saline Royale/Ledoux Foundation's computer lab. There he worked on The Computer Virus Project, his first artistic experiment with computer viruses and computer virus animation. He exhibited computer-robotic paintings at Documenta 8 in 1987. In 2002 he extended his experimentation into viral artificial life through a collaboration with the programmer Stephane Sikora of music2eye in a work called the Computer Virus Project II. Nechvatal has also created a noise music work called viral symphOny, a collaborative sound symphony created by using his computer virus software at the Institute for Electronic Arts at Alfred University. In 2021 Pentiments released Nechvatal's retrospective audio cassette called Selected Sound Works (1981-2021) and in 2022 his The Viral Tempest, a double vinyl LP of new audio work. In 2025, he joined the roster of artists/musicians at Table of the Elements with two CD/book releases: Selected Sound Works (1981-2021) and The Marriage of Orlando and Artaud, Even. From 1999 to 2013, Nechvatal taught art theories of immersive virtual reality and the viractual at the School of Visual Arts in New York City (SVA). A book of his collected essays entitled Towards an Immersive Intelligence: Essays on the Work of Art in the Age of Computer Technology and Virtual Reality (1993–2006) was published by Edgewise Press in 2009. Also in 2009, his virtual reality art theory and art history book Immersive Ideals / Critical Distances was published. In 2011, his book Immersion Into Noise was published by Open Humanities Press in conjunction with the University of Michigan Library's Scholarly Publishing Office. Nechvatal has also published three books with Punctum Books: Minóy (noise music—ed.—2014), Destroyer of Naivetés (poetry—2015), and Styling Sagaciousness (poetry—2022). In 2023 his art theory cybersex farce novella venus©~Ñ~vibrator, even was published by Orbis Tertius Press The Joseph Nechvatal archive is housed at The Fales Library Downtown Collection at the NYU Special Collections Library in New York City. === Viractualism === Viractualism is an art theory concept developed by Nechvatal in 1999 from Ph.D. research Nechvatal conducted at the Planetary Collegium at University of Wales, Newport. There he developed his concept of the viractual, which strives to create an interface between the actual and the virtual.

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  Random (software)

  Random was an iOS mobile app that used algorithms and human-curation to create an adaptive interface to the Internet. The app served a remix of relevance and serendipity that allowed people to find diverse topics and interesting content that they might not have encountered otherwise. Random did not require a login or sign-up - the use of the app was anonymous. The app was powered by an artificial intelligence that learned from direct and indirect user interactions inside the app. While learning and adapting to a person, Random created a unique anonymous choice profile that was then used for recommending topics and content. The app didn't recommend the same content twice. == User interface == Random's user interface was made of ever-changing topic blocks that contained keywords and images. By choosing any of the blocks, the user would see related web content. By closing the web content, the user could access new related topics. The user interface allowed people to get more information about a specific topic area or then just leap freely from topic to topic. The content recommended by Random could be any type of web content, varying from news articles to long-form stories and from photographs to videos. Every user of the Random was curating content for other users by using the app. == History == Random was launched in March 2014. The startup was backed by Skype co-founder Janus Friis. The Random app received a strong reception from the likes of The New York Times, TechCrunch, New Scientist, Vice, and other leading publications. The app went on to gain traction with an active and loyal user community of several hundreds of thousands. This was not enough to support the free app model the team strongly believed in, and the service was terminated in December 2015. == Reception == Various reviews in media have emphasized that Random enables people to break their filter bubble and find diverse content they might not find elsewhere. Alan Henry of Lifehacker wrote: "Random... breaks you out by intentionally guiding you to new topics and interesting articles at sites you may not otherwise read." Vice Motherboard's Claire Evans says that: "Random never turns into a filter bubble, because it perpetually injects the irrational into my experience… in a cocktail of relevancy and serendipity." The app has been said to have a unique, minimalistic user experience. Kit Eaton of The New York Times commented that Random "let's you browse the news in a different way to all the other news sites you've probably ever used." Mashable reviewed Random by concluding that the "app may be one of the most simple content-discovery apps on the market."

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  Pruning (artificial neural network)

  In deep learning, pruning is the practice of removing parameters from an existing artificial neural network. The goal of this process is to reduce the size (parameter count) of the neural network (and therefore the computational resources required to run it) whilst maintaining accuracy. This can be compared to the biological process of synaptic pruning which takes place in mammalian brains during development. == Node (neuron) pruning == A basic algorithm for pruning is as follows: Evaluate the importance of each neuron. Rank the neurons according to their importance (assuming there is a clearly defined measure for "importance"). Remove the least important neuron. Check a termination condition (to be determined by the user) to see whether to continue pruning. == Edge (weight) pruning == Most work on neural network pruning does not remove full neurons or layers (structured pruning). Instead, it focuses on removing the most insignificant weights (unstructured pruning), namely, setting their values to zero. This can either be done globally by comparing weights from all layers in the network or locally by comparing weights in each layer separately. Different metrics can be used to measure the importance of each weight. Weight magnitude as well as combinations of weight and gradient information are commonly used metrics. Early work suggested also to change the values of non-pruned weights. == When to prune the neural network? == Pruning can be applied at three different stages: before training, during training, or after training. When pruning is performed during or after training, additional fine-tuning epochs are typically required. Each approach involves different trade-offs between accuracy and computational cost.

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  Swish function

  The swish function is a family of mathematical function defined as follows: swish β ⁡ ( x ) = x sigmoid ⁡ ( β x ) = x 1 + e − β x . {\displaystyle \operatorname {swish} _{\beta }(x)=x\operatorname {sigmoid} (\beta x)={\frac {x}{1+e^{-\beta x}}}.} where β {\displaystyle \beta } can be constant (usually set to 1) or trainable and "sigmoid" refers to the logistic function. The swish family was designed to smoothly interpolate between a linear function and the Rectified linear unit (ReLU) function. When considering positive values, Swish is a particular case of doubly parameterized sigmoid shrinkage function defined in . Variants of the swish function include Mish. == Special values == For β = 0, the function is linear: f(x) = x/2. For β = 1, the function is the Sigmoid Linear Unit (SiLU). For β = 1.702, the function approximates GeLU. With β → ∞, the function converges to ReLU. Thus, the swish family smoothly interpolates between a linear function and the ReLU function. Since swish β ⁡ ( x ) = swish 1 ⁡ ( β x ) / β {\displaystyle \operatorname {swish} _{\beta }(x)=\operatorname {swish} _{1}(\beta x)/\beta } , all instances of swish have the same shape as the default swish 1 {\displaystyle \operatorname {swish} _{1}} , zoomed by β {\displaystyle \beta } . One usually sets β > 0 {\displaystyle \beta >0} . When β {\displaystyle \beta } is trainable, this constraint can be enforced by β = e b {\displaystyle \beta =e^{b}} , where b {\displaystyle b} is trainable. swish 1 ⁡ ( x ) = x 2 + x 2 4 − x 4 48 + x 6 480 + O ( x 8 ) {\displaystyle \operatorname {swish} _{1}(x)={\frac {x}{2}}+{\frac {x^{2}}{4}}-{\frac {x^{4}}{48}}+{\frac {x^{6}}{480}}+O\left(x^{8}\right)} swish 1 ⁡ ( x ) = x 2 tanh ⁡ ( x 2 ) + x 2 swish 1 ⁡ ( x ) + swish − 1 ⁡ ( x ) = x tanh ⁡ ( x 2 ) swish 1 ⁡ ( x ) − swish − 1 ⁡ ( x ) = x {\displaystyle {\begin{aligned}\operatorname {swish} _{1}(x)&={\frac {x}{2}}\tanh \left({\frac {x}{2}}\right)+{\frac {x}{2}}\\\operatorname {swish} _{1}(x)+\operatorname {swish} _{-1}(x)&=x\tanh \left({\frac {x}{2}}\right)\\\operatorname {swish} _{1}(x)-\operatorname {swish} _{-1}(x)&=x\end{aligned}}} == Derivatives == Because swish β ⁡ ( x ) = swish 1 ⁡ ( β x ) / β {\displaystyle \operatorname {swish} _{\beta }(x)=\operatorname {swish} _{1}(\beta x)/\beta } , it suffices to calculate its derivatives for the default case. swish 1 ′ ⁡ ( x ) = x + sinh ⁡ ( x ) 4 cosh 2 ⁡ ( x 2 ) + 1 2 {\displaystyle \operatorname {swish} _{1}'(x)={\frac {x+\sinh(x)}{4\cosh ^{2}\left({\frac {x}{2}}\right)}}+{\frac {1}{2}}} so swish 1 ′ ⁡ ( x ) − 1 2 {\displaystyle \operatorname {swish} _{1}'(x)-{\frac {1}{2}}} is odd. swish 1 ″ ⁡ ( x ) = 1 − x 2 tanh ⁡ ( x 2 ) 2 cosh 2 ⁡ ( x 2 ) {\displaystyle \operatorname {swish} _{1}''(x)={\frac {1-{\frac {x}{2}}\tanh \left({\frac {x}{2}}\right)}{2\cosh ^{2}\left({\frac {x}{2}}\right)}}} so swish 1 ″ ⁡ ( x ) {\displaystyle \operatorname {swish} _{1}''(x)} is even. == History == SiLU was first proposed alongside the GELU in 2016, then again proposed in 2017 as the Sigmoid-weighted Linear Unit (SiL) in reinforcement learning. The SiLU/SiL was then again proposed as the SWISH over a year after its initial discovery, originally proposed without the learnable parameter β, so that β implicitly equaled 1. The swish paper was then updated to propose the activation with the learnable parameter β. In 2017, after performing analysis on ImageNet data, researchers from Google indicated that using this function as an activation function in artificial neural networks improves the performance, compared to ReLU and sigmoid functions. It is believed that one reason for the improvement is that the swish function helps alleviate the vanishing gradient problem during backpropagation.

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  Evolutionary algorithm

  Evolutionary algorithms (EA) reproduce essential elements of biological evolution in a computer algorithm in order to solve "difficult" problems, at least approximately, for which no exact or satisfactory solution methods are known. They are metaheuristics and population-based bio-inspired algorithms and evolutionary computation, which itself are part of the field of computational intelligence. The mechanisms of biological evolution that an EA mainly imitates are reproduction, mutation, recombination and selection. Candidate solutions to the optimization problem play the role of individuals in a population, and the fitness function determines the quality of the solutions (see also loss function). Evolution of the population then takes place after the repeated application of the above operators. Evolutionary algorithms often perform well approximating solutions to all types of problems because they ideally do not make any assumption about the underlying fitness landscape. Techniques from evolutionary algorithms applied to the modeling of biological evolution are generally limited to explorations of microevolution (microevolutionary processes) and planning models based upon cellular processes. In most real applications of EAs, computational complexity is a prohibiting factor. In fact, this computational complexity is due to fitness function evaluation. Fitness approximation is one of the solutions to overcome this difficulty. However, seemingly simple EA can solve often complex problems; therefore, there may be no direct link between algorithm complexity and problem complexity. == Generic definition == The following is an example of a generic evolutionary algorithm: Randomly generate the initial population of individuals, the first generation. Evaluate the fitness of each individual in the population. Check, if the goal is reached and the algorithm can be terminated. Select individuals as parents, preferably of higher fitness. Produce offspring with optional crossover (mimicking reproduction). Apply mutation operations on the offspring. Select individuals preferably of lower fitness for replacement with new individuals (mimicking natural selection). Return to 2 == Types == Similar techniques differ in genetic representation and other implementation details, and the nature of the particular applied problem. Genetic algorithm – This is the most popular type of EA. One seeks the solution of a problem in the form of strings of numbers (traditionally binary, although the best representations are usually those that reflect something about the problem being solved), by applying operators such as recombination and mutation (sometimes one, sometimes both). This type of EA is often used in optimization problems. Genetic programming – Here the solutions are in the form of computer programs, and their fitness is determined by their ability to solve a computational problem. There are many variants of Genetic Programming: Cartesian genetic programming Gene expression programming Grammatical evolution Linear genetic programming Multi expression programming Evolutionary programming – Similar to evolution strategy, but with a deterministic selection of all parents. Evolution strategy (ES) – Works with vectors of real numbers as representations of solutions, and typically uses self-adaptive mutation rates. The method is mainly used for numerical optimization, although there are also variants for combinatorial tasks. CMA-ES Natural evolution strategy Differential evolution – Based on vector differences and is therefore primarily suited for numerical optimization problems. Coevolutionary algorithm – Similar to genetic algorithms and evolution strategies, but the created solutions are compared on the basis of their outcomes from interactions with other solutions. Solutions can either compete or cooperate during the search process. Coevolutionary algorithms are often used in scenarios where the fitness landscape is dynamic, complex, or involves competitive interactions. Neuroevolution – Similar to genetic programming but the genomes represent artificial neural networks by describing structure and connection weights. The genome encoding can be direct or indirect. Learning classifier system – Here the solution is a set of classifiers (rules or conditions). A Michigan-LCS evolves at the level of individual classifiers whereas a Pittsburgh-LCS uses populations of classifier-sets. Initially, classifiers were only binary, but now include real, neural net, or S-expression types. Fitness is typically determined with either a strength or accuracy based reinforcement learning or supervised learning approach. Quality–Diversity algorithms – QD algorithms simultaneously aim for high-quality and diverse solutions. Unlike traditional optimization algorithms that solely focus on finding the best solution to a problem, QD algorithms explore a wide variety of solutions across a problem space and keep those that are not just high performing, but also diverse and unique. == Theoretical background == The following theoretical principles apply to all or almost all EAs. === No free lunch theorem === The no free lunch theorem of optimization states that all optimization strategies are equally effective when the set of all optimization problems is considered. Under the same condition, no evolutionary algorithm is fundamentally better than another. This can only be the case if the set of all problems is restricted. This is exactly what is inevitably done in practice. Therefore, to improve an EA, it must exploit problem knowledge in some form (e.g. by choosing a certain mutation strength or a problem-adapted coding). Thus, if two EAs are compared, this constraint is implied. In addition, an EA can use problem specific knowledge by, for example, not randomly generating the entire start population, but creating some individuals through heuristics or other procedures. Another possibility to tailor an EA to a given problem domain is to involve suitable heuristics, local search procedures or other problem-related procedures in the process of generating the offspring. This form of extension of an EA is also known as a memetic algorithm. Both extensions play a major role in practical applications, as they can speed up the search process and make it more robust. === Convergence === For EAs in which, in addition to the offspring, at least the best individual of the parent generation is used to form the subsequent generation (so-called elitist EAs), there is a general proof of convergence under the condition that an optimum exists. Without loss of generality, a maximum search is assumed for the proof: From the property of elitist offspring acceptance and the existence of the optimum it follows that per generation k {\displaystyle k} an improvement of the fitness F {\displaystyle F} of the respective best individual x ′ {\displaystyle x'} will occur with a probability P > 0 {\displaystyle P>0} . Thus: F ( x 1 ′ ) ≤ F ( x 2 ′ ) ≤ F ( x 3 ′ ) ≤ ⋯ ≤ F ( x k ′ ) ≤ ⋯ {\displaystyle F(x'_{1})\leq F(x'_{2})\leq F(x'_{3})\leq \cdots \leq F(x'_{k})\leq \cdots } I.e., the fitness values represent a monotonically non-decreasing sequence, which is bounded due to the existence of the optimum. From this follows the convergence of the sequence against the optimum. Since the proof makes no statement about the speed of convergence, it is of little help in practical applications of EAs. But it does justify the recommendation to use elitist EAs. However, when using the usual panmictic population model, elitist EAs tend to converge prematurely more than non-elitist ones. In a panmictic population model, mate selection (see step 4 of the generic definition) is such that every individual in the entire population is eligible as a mate. In non-panmictic populations, selection is suitably restricted, so that the dispersal speed of better individuals is reduced compared to panmictic ones. Thus, the general risk of premature convergence of elitist EAs can be significantly reduced by suitable population models that restrict mate selection. === Virtual alphabets === With the theory of virtual alphabets, David E. Goldberg showed in 1990 that by using a representation with real numbers, an EA that uses classical recombination operators (e.g. uniform or n-point crossover) cannot reach certain areas of the search space, in contrast to a coding with binary numbers. This results in the recommendation for EAs with real representation to use arithmetic operators for recombination (e.g. arithmetic mean or intermediate recombination). With suitable operators, real-valued representations are more effective than binary ones, contrary to earlier opinion. == Comparison to other concepts == === Biological processes === A possible limitation of many evolutionary algorithms is their lack of a clear genotype–phenotype distinction. In nature, the fertilized egg cell undergoes a complex process known as embryogenesis to become a mature p

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  Open information extraction

  In natural language processing, open information extraction (OIE) is the task of generating a structured, machine-readable representation of the information in text, usually in the form of triples or n-ary propositions. == Overview == A proposition can be understood as truth-bearer, a textual expression of a potential fact (e.g., "Dante wrote the Divine Comedy"), represented in an amenable structure for computers [e.g., ("Dante", "wrote", "Divine Comedy")]. An OIE extraction normally consists of a relation and a set of arguments. For instance, ("Dante", "passed away in" "Ravenna") is a proposition formed by the relation "passed away in" and the arguments "Dante" and "Ravenna". The first argument is usually referred as the subject while the second is considered to be the object. The extraction is said to be a textual representation of a potential fact because its elements are not linked to a knowledge base. Furthermore, the factual nature of the proposition has not yet been established. In the above example, transforming the extraction into a full fledged fact would first require linking, if possible, the relation and the arguments to a knowledge base. Second, the truth of the extraction would need to be determined. In computer science transforming OIE extractions into ontological facts is known as relation extraction. In fact, OIE can be seen as the first step to a wide range of deeper text understanding tasks such as relation extraction, knowledge-base construction, question answering, semantic role labeling. The extracted propositions can also be directly used for end-user applications such as structured search (e.g., retrieve all propositions with "Dante" as subject). OIE was first introduced by TextRunner developed at the University of Washington Turing Center headed by Oren Etzioni. Other methods introduced later such as Reverb, OLLIE, ClausIE or CSD helped to shape the OIE task by characterizing some of its aspects. At a high level, all of these approaches make use of a set of patterns to generate the extractions. Depending on the particular approach, these patterns are either hand-crafted or learned. == OIE systems and contributions == Reverb suggested the necessity to produce meaningful relations to more accurately capture the information in the input text. For instance, given the sentence "Faust made a pact with the devil", it would be erroneous to just produce the extraction ("Faust", "made", "a pact") since it would not be adequately informative. A more precise extraction would be ("Faust", "made a pact with", "the devil"). Reverb also argued against the generation of overspecific relations. OLLIE stressed two important aspects for OIE. First, it pointed to the lack of factuality of the propositions. For instance, in a sentence like "If John studies hard, he will pass the exam", it would be inaccurate to consider ("John", "will pass", "the exam") as a fact. Additionally, the authors indicated that an OIE system should be able to extract non-verb mediated relations, which account for significant portion of the information expressed in natural language text. For instance, in the sentence "Obama, the former US president, was born in Hawaii", an OIE system should be able to recognize a proposition ("Obama", "is", "former US president"). ClausIE introduced the connection between grammatical clauses, propositions, and OIE extractions. The authors stated that as each grammatical clause expresses a proposition, each verb mediated proposition can be identified by solely recognizing the set of clauses expressed in each sentence. This implies that to correctly recognize the set of propositions in an input sentence, it is necessary to understand its grammatical structure. The authors studied the case in the English language that only admits seven clause types, meaning that the identification of each proposition only requires defining seven grammatical patterns. The finding also established a separation between the recognition of the propositions and its materialization. In a first step, the proposition can be identified without any consideration of its final form, in a domain-independent and unsupervised way, mostly based on linguistic principles. In a second step, the information can be represented according to the requirements of the underlying application, without conditioning the identification phase. Consider the sentence "Albert Einstein was born in Ulm and died in Princeton". The first step will recognize the two propositions ("Albert Einstein", "was born", "in Ulm") and ("Albert Einstein", "died", "in Princeton"). Once the information has been correctly identified, the propositions can take the particular form required by the underlying application [e.g., ("Albert Einstein", "was born in", "Ulm") and ("Albert Einstein", "died in", "Princeton")]. CSD introduced the idea of minimality in OIE. It considers that computers can make better use of the extractions if they are expressed in a compact way. This is especially important in sentences with subordinate clauses. In these cases, CSD suggests the generation of nested extractions. For example, consider the sentence "The Embassy said that 6,700 Americans were in Pakistan". CSD generates two extractions [i] ("6,700 Americans", "were", "in Pakistan") and [ii] ("The Embassy", "said", "that [i]"). This is usually known as reification.

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  Recursive neural network

  A recursive neural network is a kind of deep neural network created by applying the same set of weights recursively over a structured input, to produce a structured prediction over variable-size input structures, or a scalar prediction on it, by traversing a given structure in topological order. These networks were first introduced to learn distributed representations of structure (such as logical terms), but have been successful in multiple applications, for instance in learning sequence and tree structures in natural language processing (mainly continuous representations of phrases and sentences based on word embeddings). == Architectures == === Basic === In the simplest architecture, nodes are combined into parents using a weight matrix (which is shared across the whole network) and a non-linearity such as the tanh {\displaystyle \tanh } hyperbolic function. If c 1 {\displaystyle c_{1}} and c 2 {\displaystyle c_{2}} are n {\displaystyle n} -dimensional vector representations of nodes, their parent will also be an n {\displaystyle n} -dimensional vector, defined as: p 1 , 2 = tanh ⁡ ( W [ c 1 ; c 2 ] ) {\displaystyle p_{1,2}=\tanh(W[c_{1};c_{2}])} where W {\displaystyle W} is a learned n × 2 n {\displaystyle n\times 2n} weight matrix. This architecture, with a few improvements, has been used for successfully parsing natural scenes, syntactic parsing of natural language sentences, and recursive autoencoding and generative modeling of 3D shape structures in the form of cuboid abstractions. === Recursive cascade correlation (RecCC) === RecCC is a constructive neural network approach to deal with tree domains with pioneering applications to chemistry and extension to directed acyclic graphs. === Unsupervised RNN === A framework for unsupervised RNN has been introduced in 2004. === Tensor === Recursive neural tensor networks use a single tensor-based composition function for all nodes in the tree. == Training == === Stochastic gradient descent === Typically, stochastic gradient descent (SGD) is used to train the network. The gradient is computed using backpropagation through structure (BPTS), a variant of backpropagation through time used for recurrent neural networks. == Properties == The universal approximation capability of RNNs over trees has been proved in literature. == Related models == === Recurrent neural networks === Recurrent neural networks are recursive artificial neural networks with a certain structure: that of a linear chain. Whereas recursive neural networks operate on any hierarchical structure, combining child representations into parent representations, recurrent neural networks operate on the linear progression of time, combining the previous time step and a hidden representation into the representation for the current time step. === Tree Echo State Networks === An efficient approach to implement recursive neural networks is given by the Tree Echo State Network within the reservoir computing paradigm. === Extension to graphs === Extensions to graphs include graph neural network (GNN), Neural Network for Graphs (NN4G), and more recently convolutional neural networks for graphs.

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  Diffusion map

  Diffusion maps is a dimensionality reduction or feature extraction algorithm introduced by Coifman and Lafon which computes a family of embeddings of a data set into Euclidean space (often low-dimensional) whose coordinates can be computed from the eigenvectors and eigenvalues of a diffusion operator on the data. The Euclidean distance between points in the embedded space is equal to the "diffusion distance" between probability distributions centered at those points. Different from linear dimensionality reduction methods such as principal component analysis (PCA), diffusion maps are part of the family of nonlinear dimensionality reduction methods which focus on discovering the underlying manifold that the data has been sampled from. By integrating local similarities at different scales, diffusion maps give a global description of the data-set. Compared with other methods, the diffusion map algorithm is robust to noise perturbation and computationally inexpensive. == Definition of diffusion maps == Following and , diffusion maps can be defined in four steps. === Connectivity === Diffusion maps exploit the relationship between heat diffusion and random walk Markov chain. The basic observation is that if we take a random walk on the data, walking to a nearby data-point is more likely than walking to another that is far away. Let ( X , A , μ ) {\displaystyle (X,{\mathcal {A}},\mu )} be a measure space, where X {\displaystyle X} is the data set and μ {\displaystyle \mu } represents the distribution of the points on X {\displaystyle X} . Based on this, the connectivity k {\displaystyle k} between two data points, x {\displaystyle x} and y {\displaystyle y} , can be defined as the probability of walking from x {\displaystyle x} to y {\displaystyle y} in one step of the random walk. Usually, this probability is specified in terms of a kernel function of the two points: k : X × X → R {\displaystyle k:X\times X\rightarrow \mathbb {R} } . For example, the popular Gaussian kernel: k ( x , y ) = exp ⁡ ( − | | x − y | | 2 ϵ ) {\displaystyle k(x,y)=\exp \left(-{\frac {||x-y||^{2}}{\epsilon }}\right)} More generally, the kernel function has the following properties k ( x , y ) = k ( y , x ) {\displaystyle k(x,y)=k(y,x)} ( k {\displaystyle k} is symmetric) k ( x , y ) ≥ 0 ∀ x , y {\displaystyle k(x,y)\geq 0\,\,\forall x,y} ( k {\displaystyle k} is positivity preserving). The kernel constitutes the prior definition of the local geometry of the data-set. Since a given kernel will capture a specific feature of the data set, its choice should be guided by the application that one has in mind. This is a major difference with methods such as principal component analysis, where correlations between all data points are taken into account at once. Given ( X , k ) {\displaystyle (X,k)} , we can then construct a reversible discrete-time Markov chain on X {\displaystyle X} (a process known as the normalized graph Laplacian construction): d ( x ) = ∫ X k ( x , y ) d μ ( y ) {\displaystyle d(x)=\int _{X}k(x,y)d\mu (y)} and define: p ( x , y ) = k ( x , y ) d ( x ) {\displaystyle p(x,y)={\frac {k(x,y)}{d(x)}}} Although the new normalized kernel does not inherit the symmetric property, it does inherit the positivity-preserving property and gains a conservation property: ∫ X p ( x , y ) d μ ( y ) = 1 {\displaystyle \int _{X}p(x,y)d\mu (y)=1} === Diffusion process === From p ( x , y ) {\displaystyle p(x,y)} we can construct a transition matrix of a Markov chain ( M {\displaystyle M} ) on X {\displaystyle X} . In other words, p ( x , y ) {\displaystyle p(x,y)} represents the one-step transition probability from x {\displaystyle x} to y {\displaystyle y} , and M t {\displaystyle M^{t}} gives the t-step transition matrix. We define the diffusion matrix L {\displaystyle L} (it is also a version of graph Laplacian matrix) L i , j = k ( x i , x j ) {\displaystyle L_{i,j}=k(x_{i},x_{j})\,} We then define the new kernel L i , j ( α ) = k ( α ) ( x i , x j ) = L i , j ( d ( x i ) d ( x j ) ) α {\displaystyle L_{i,j}^{(\alpha )}=k^{(\alpha )}(x_{i},x_{j})={\frac {L_{i,j}}{(d(x_{i})d(x_{j}))^{\alpha }}}\,} or equivalently, L ( α ) = D − α L D − α {\displaystyle L^{(\alpha )}=D^{-\alpha }LD^{-\alpha }\,} where D is a diagonal matrix and D i , i = ∑ j L i , j . {\displaystyle D_{i,i}=\sum _{j}L_{i,j}.} We apply the graph Laplacian normalization to this new kernel: M = ( D ( α ) ) − 1 L ( α ) , {\displaystyle M=({D}^{(\alpha )})^{-1}L^{(\alpha )},\,} where D ( α ) {\displaystyle D^{(\alpha )}} is a diagonal matrix and D i , i ( α ) = ∑ j L i , j ( α ) . {\displaystyle {D}_{i,i}^{(\alpha )}=\sum _{j}L_{i,j}^{(\alpha )}.} p ( x j , t | x i ) = M i , j t {\displaystyle p(x_{j},t|x_{i})=M_{i,j}^{t}\,} One of the main ideas of the diffusion framework is that running the chain forward in time (taking larger and larger powers of M {\displaystyle M} ) reveals the geometric structure of X {\displaystyle X} at larger and larger scales (the diffusion process). Specifically, the notion of a cluster in the data set is quantified as a region in which the probability of escaping this region is low (within a certain time t). Therefore, t not only serves as a time parameter, but it also has the dual role of scale parameter. The eigendecomposition of the matrix M t {\displaystyle M^{t}} yields M i , j t = ∑ l λ l t ψ l ( x i ) ϕ l ( x j ) {\displaystyle M_{i,j}^{t}=\sum _{l}\lambda _{l}^{t}\psi _{l}(x_{i})\phi _{l}(x_{j})\,} where { λ l } {\displaystyle \{\lambda _{l}\}} is the sequence of eigenvalues of M {\displaystyle M} and { ψ l } {\displaystyle \{\psi _{l}\}} and { ϕ l } {\displaystyle \{\phi _{l}\}} are the biorthogonal left and right eigenvectors respectively. Due to the spectrum decay of the eigenvalues, only a few terms are necessary to achieve a given relative accuracy in this sum. ==== Parameter α and the diffusion operator ==== The reason to introduce the normalization step involving α {\displaystyle \alpha } is to tune the influence of the data point density on the infinitesimal transition of the diffusion. In some applications, the sampling of the data is generally not related to the geometry of the manifold we are interested in describing. In this case, we can set α = 1 {\displaystyle \alpha =1} and the diffusion operator approximates the Laplace–Beltrami operator. We then recover the Riemannian geometry of the data set regardless of the distribution of the points. To describe the long-term behavior of the point distribution of a system of stochastic differential equations, we can use α = 0.5 {\displaystyle \alpha =0.5} and the resulting Markov chain approximates the Fokker–Planck diffusion. With α = 0 {\displaystyle \alpha =0} , it reduces to the classical graph Laplacian normalization. === Diffusion distance === The diffusion distance at time t {\displaystyle t} between two points can be measured as the similarity of two points in the observation space with the connectivity between them. It is given by D t ( x i , x j ) 2 = ∑ y ( p ( y , t | x i ) − p ( y , t | x j ) ) 2 ϕ 0 ( y ) {\displaystyle D_{t}(x_{i},x_{j})^{2}=\sum _{y}{\frac {(p(y,t|x_{i})-p(y,t|x_{j}))^{2}}{\phi _{0}(y)}}} where ϕ 0 ( y ) {\displaystyle \phi _{0}(y)} is the stationary distribution of the Markov chain, given by the first left eigenvector of M {\displaystyle M} . Explicitly: ϕ 0 ( y ) = d ( y ) ∑ z ∈ X d ( z ) {\displaystyle \phi _{0}(y)={\frac {d(y)}{\sum _{z\in X}d(z)}}} Intuitively, D t ( x i , x j ) {\displaystyle D_{t}(x_{i},x_{j})} is small if there is a large number of short paths connecting x i {\displaystyle x_{i}} and x j {\displaystyle x_{j}} . There are several interesting features associated with the diffusion distance, based on our previous discussion that t {\displaystyle t} also serves as a scale parameter: Points are closer at a given scale (as specified by D t ( x i , x j ) {\displaystyle D_{t}(x_{i},x_{j})} ) if they are highly connected in the graph, therefore emphasizing the concept of a cluster. This distance is robust to noise, since the distance between two points depends on all possible paths of length t {\displaystyle t} between the points. From a machine learning point of view, the distance takes into account all evidences linking x i {\displaystyle x_{i}} to x j {\displaystyle x_{j}} , allowing us to conclude that this distance is appropriate for the design of inference algorithms based on the majority of preponderance. === Diffusion process and low-dimensional embedding === The diffusion distance can be calculated using the eigenvectors by D t ( x i , x j ) 2 = ∑ l λ l 2 t ( ψ l ( x i ) − ψ l ( x j ) ) 2 {\displaystyle D_{t}(x_{i},x_{j})^{2}=\sum _{l}\lambda _{l}^{2t}(\psi _{l}(x_{i})-\psi _{l}(x_{j}))^{2}\,} So the eigenvectors can be used as a new set of coordinates for the data. The diffusion map is defined as: Ψ t ( x ) = ( λ 1 t ψ 1 ( x ) , λ 2 t ψ 2 ( x ) , … , λ k t ψ k ( x ) ) {\displaystyle \Psi _{t}(x)=(\lambda _{1}^{t}\psi _{1}(x),\lambda _{2}^{t}\psi _{2}(x),\ld

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  U-matrix

  The U-matrix (unified distance matrix) is a representation of a self-organizing map (SOM) where the Euclidean distance between the codebook vectors of neighboring neurons is depicted in a grayscale image. This image is used to visualize the data in a high-dimensional space using a 2D image. == Construction procedure == Once the SOM is trained using the input data, the final map is not expected to have any twists. If the map is twist-free, the distance between the codebook vectors of neighboring neurons gives an approximation of the distance between different parts of the underlying data. When such distances are depicted in a grayscale image, light colors depict closely spaced node codebook vectors and darker colors indicate more widely separated node codebook vectors. Thus, groups of light colors can be considered as clusters, and the dark parts as the boundaries between the clusters. This representation can help to visualize the clusters in the high-dimensional spaces, or to automatically recognize them using relatively simple image processing techniques.

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  Time series

  In mathematics, a time series is a sequence of data points indexed, listed, or graphed in chronological order. Most commonly, a time series consists of observations recorded at successive equally spaced points in time. Thus, it represents a form of discrete-time data. A time series may describe measurements collected over seconds, days, years, or even centuries. Common examples include heights of ocean tides, counts of sunspots, daily temperature readings, and the closing values of stock market indices such as the Dow Jones Industrial Average. A time series is often visualized using a run chart (a type of temporal line chart), which helps identify patterns such as trends, seasonal effects, and irregular fluctuations. Time series are widely used in statistics, actuarial science, signal processing, pattern recognition, econometrics, mathematical finance, weather forecasting, earthquake prediction, electroencephalography, control engineering, astronomy, communications engineering, and many other areas of applied science and engineering that involve temporal measurements. Time series analysis comprises methods for analyzing time series data in order to extract meaningful statistics and other characteristics of the data. Time series forecasting is the use of a model to predict future values based on previously observed values. Generally, time series data is modeled as a stochastic process. While regression analysis is often employed in such a way as to test relationships between one or more different time series, this type of analysis is not usually called "time series analysis", which refers in particular to relationships between different points in time within a single series. Time series data have a natural temporal ordering. This makes time series analysis distinct from cross-sectional studies, in which there is no natural ordering of the observations (e.g. explaining people's wages by reference to their respective education levels, where the individuals' data could be entered in any order). Time series analysis is also distinct from spatial data analysis where the observations typically relate to geographical locations (e.g. accounting for house prices by the location as well as the intrinsic characteristics of the houses). A stochastic model for a time series will generally reflect the fact that observations close together in time will be more closely related than observations further apart. In addition, time series models will often make use of the natural one-way ordering of time so that values for a given period will be expressed as deriving in some way from past values, rather than from future values (see time reversibility). Time series analysis can be applied to real-valued, continuous data, discrete numeric data, or discrete symbolic data (i.e. sequences of characters, such as letters and words in the English language). == Methods for analysis == Methods for time series analysis may be divided into two classes: frequency-domain methods and time-domain methods. The former include spectral analysis and wavelet analysis; the latter include auto-correlation and cross-correlation analysis. In the time domain, correlation and analysis can be made in a filter-like manner using scaled correlation, thereby mitigating the need to operate in the frequency domain. Additionally, time series analysis techniques may be divided into parametric and non-parametric methods. The parametric approaches assume that the underlying stationary stochastic process has a certain structure which can be described using a small number of parameters (for example, using an autoregressive or moving-average model). In these approaches, the task is to estimate the parameters of the model that describes the stochastic process. By contrast, non-parametric approaches explicitly estimate the covariance or the spectrum of the process without assuming that the process has any particular structure. Methods of time series analysis may also be divided into linear and non-linear, and univariate and multivariate. == Panel data == A time series is one type of panel data. Panel data is the general class, a multidimensional data set, whereas a time series data set is a one-dimensional panel (as is a cross-sectional dataset). A data set may exhibit characteristics of both panel data and time series data. One way to tell is to ask what makes one data record unique from the other records. If the answer is the time data field, then this is a time series data set candidate. If determining a unique record requires a time data field and an additional identifier which is unrelated to time (e.g. student ID, stock symbol, country code), then it is panel data candidate. If the differentiation lies on the non-time identifier, then the data set is a cross-sectional data set candidate. == Analysis == There are several types of motivation and data analysis available for time series which are appropriate for different purposes. === Motivation === In the context of statistics, econometrics, quantitative finance, seismology, meteorology, and geophysics the primary goal of time series analysis is forecasting. In the context of signal processing, control engineering and communication engineering it is used for signal detection. Other applications are in data mining, pattern recognition and machine learning, where time series analysis can be used for clustering, classification, query by content, anomaly detection as well as forecasting. === Exploratory analysis === A simple way to examine a regular time series is manually with a line chart. The datagraphic shows tuberculosis deaths in the United States, along with the yearly change and the percentage change from year to year. The total number of deaths declined in every year until the mid-1980s, after which there were occasional increases, often proportionately - but not absolutely - quite large. A study of corporate data analysts found two challenges to exploratory time series analysis: discovering the shape of interesting patterns, and finding an explanation for these patterns. Visual tools that represent time series data as heat map matrices can help overcome these challenges. === Estimation, filtering, and smoothing === This approach may be based on harmonic analysis and filtering of signals in the frequency domain using the Fourier transform, and spectral density estimation. Its development was significantly accelerated during World War II by mathematician Norbert Wiener, electrical engineers Rudolf E. Kálmán, Dennis Gabor and others for filtering signals from noise and predicting signal values at a certain point in time. An equivalent effect may be achieved in the time domain, as in a Kalman filter; see filtering and smoothing for more techniques. Other related techniques include: Autocorrelation analysis to examine serial dependence Spectral analysis to examine cyclic behavior which need not be related to seasonality. For example, sunspot activity varies over 11 year cycles. Other common examples include celestial phenomena, weather patterns, neural activity, commodity prices, and economic activity. Separation into components representing trend, seasonality, slow and fast variation, and cyclical irregularity: see trend estimation and decomposition of time series === Curve fitting === Curve fitting is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, possibly subject to constraints. Curve fitting can involve either interpolation, where an exact fit to the data is required, or smoothing, in which a "smooth" function is constructed that approximately fits the data. A related topic is regression analysis, which focuses more on questions of statistical inference such as how much uncertainty is present in a curve that is fit to data observed with random errors. Fitted curves can be used as an aid for data visualization, to infer values of a function where no data are available, and to summarize the relationships among two or more variables. Extrapolation refers to the use of a fitted curve beyond the range of the observed data, and is subject to a degree of uncertainty since it may reflect the method used to construct the curve as much as it reflects the observed data. For processes that are expected to generally grow in magnitude one of the curves in the graphic (and many others) can be fitted by estimating their parameters. The construction of economic time series involves the estimation of some components for some dates by interpolation between values ("benchmarks") for earlier and later dates. Interpolation is estimation of an unknown quantity between two known quantities (historical data), or drawing conclusions about missing information from the available information ("reading between the lines"). Interpolation is useful where the data surrounding the missing data is available and its trend, seasonality, and longer-term cycles are known. This is often done by using a relat

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  Persian Speech Corpus

  The Persian Speech Corpus is a Modern Persian speech corpus for speech synthesis. The corpus contains phonetic and orthographic transcriptions of about 2.5 hours of Persian speech aligned with recorded speech on the phoneme level, including annotations of word boundaries. Previous spoken corpora of Persian include FARSDAT, which consists of read aloud speech from newspaper texts from 100 Persian speakers and the Telephone FARsi Spoken language DATabase (TFARSDAT) which comprises seven hours of read and spontaneous speech produced by 60 native speakers of Persian from ten regions of Iran. The Persian Speech Corpus was built using the same methodologies laid out in the doctoral project on Modern Standard Arabic of Nawar Halabi at the University of Southampton. The work was funded by MicroLinkPC, who own an exclusive license to commercialise the corpus, though the corpus is available for non-commercial use through the corpus' website. It is distributed under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. The corpus was built for speech synthesis purposes, but has been used for building HMM based voices in Persian. It can also be used to automatically align other speech corpora with their phonetic transcript and could be used as part of a larger corpus for training speech recognition systems. == Contents == The corpus is downloadable from its website, and contains the following: 396 .wav files containing spoken utterances 396 .lab files containing text utterances 396 .TextGrid files containing the phoneme labels with time stamps of the boundaries where these occur in the .wav files. phonetic-transcript.txt which has the form "[wav_filename]" "[Phoneme Sequence]" in every line orthographic-transcript.txt which has the form "[wav_filename]" "[Orthographic Transcript]" in every line

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  Ensemble learning

  In statistics and machine learning, ensemble methods use multiple learning algorithms to obtain better predictive performance than could be obtained from any of the constituent learning algorithms alone. Unlike a statistical ensemble in statistical mechanics, which is usually infinite, a machine learning ensemble consists of only a concrete finite set of alternative models, but typically allows for much more flexible structure to exist among those alternatives. == Overview == Supervised learning algorithms search through a hypothesis space to find a suitable hypothesis that will make good predictions with a particular problem. Even if this space contains hypotheses that are very well-suited for a particular problem, it may be very difficult to find a good one. Ensembles combine multiple hypotheses to form one which should be theoretically better. Ensemble learning trains two or more machine learning algorithms on a specific classification or regression task. The algorithms within the ensemble model are generally referred as "base models", "base learners", or "weak learners" in literature. These base models can be constructed using a single modelling algorithm, or several different algorithms. The idea is to train a diverse set of weak models on the same modelling task, such that the outputs of each weak learner have poor predictive ability (i.e., high bias), and among all weak learners, the outcome and error values exhibit high variance. Fundamentally, an ensemble learning model trains at least two high-bias (weak) and high-variance (diverse) models to be combined into a better-performing model. The set of weak models — which would not produce satisfactory predictive results individually — are combined or averaged to produce a single, high performing, accurate, and low-variance model to fit the task as required. Ensemble learning typically refers to bagging (bootstrap aggregating), boosting or stacking/blending techniques to induce high variance among the base models. Bagging creates diversity by generating random samples from the training observations and fitting the same model to each different sample — also known as homogeneous parallel ensembles. Boosting follows an iterative process by sequentially training each base model on the up-weighted errors of the previous base model, producing an additive model to reduce the final model errors — also known as sequential ensemble learning. Stacking or blending consists of different base models, each trained independently (i.e. diverse/high variance) to be combined into the ensemble model — producing a heterogeneous parallel ensemble. Common applications of ensemble learning include random forests (an extension of bagging), Boosted Tree models, and Gradient Boosted Tree Models. Models in applications of stacking are generally more task-specific — such as combining clustering techniques with other parametric and/or non-parametric techniques. Evaluating the prediction of an ensemble typically requires more computation than evaluating the prediction of a single model. In one sense, ensemble learning may be thought of as a way to compensate for poor learning algorithms by performing a lot of extra computation. On the other hand, the alternative is to do a lot more learning with one non-ensemble model. An ensemble may be more efficient at improving overall accuracy for the same increase in compute, storage, or communication resources by using that increase on two or more methods, than would have been improved by increasing resource use for a single method. Fast algorithms such as decision trees are commonly used in ensemble methods (e.g., random forests), although slower algorithms can benefit from ensemble techniques as well. By analogy, ensemble techniques have been used also in unsupervised learning scenarios, for example in consensus clustering or in anomaly detection. == Ensemble theory == Empirically, ensembles tend to yield better results when there is a significant diversity among the models. Many ensemble methods, therefore, seek to promote diversity among the models they combine. Although perhaps non-intuitive, more random algorithms (like random decision trees) can be used to produce a stronger ensemble than very deliberate algorithms (like entropy-reducing decision trees). Using a variety of strong learning algorithms, however, has been shown to be more effective than using techniques that attempt to dumb-down the models in order to promote diversity. It is possible to increase diversity in the training stage of the model using correlation for regression tasks or using information measures such as cross entropy for classification tasks. Theoretically, one can justify the diversity concept because the lower bound of the error rate of an ensemble system can be decomposed into accuracy, diversity, and the other term. === The geometric framework === Ensemble learning, including both regression and classification tasks, can be explained using a geometric framework. Within this framework, the output of each individual classifier or regressor for the entire dataset can be viewed as a point in a multi-dimensional space. Additionally, the target result is also represented as a point in this space, referred to as the "ideal point." The Euclidean distance is used as the metric to measure both the performance of a single classifier or regressor (the distance between its point and the ideal point) and the dissimilarity between two classifiers or regressors (the distance between their respective points). This perspective transforms ensemble learning into a deterministic problem. For example, within this geometric framework, it can be proved that the averaging of the outputs (scores) of all base classifiers or regressors can lead to equal or better results than the average of all the individual models. It can also be proved that if the optimal weighting scheme is used, then a weighted averaging approach can outperform any of the individual classifiers or regressors that make up the ensemble or as good as the best performer at least. == Ensemble size == While the number of component classifiers of an ensemble has a great impact on the accuracy of prediction, there is a limited number of studies addressing this problem. A priori determining of ensemble size and the volume and velocity of big data streams make this even more crucial for online ensemble classifiers. Mostly statistical tests were used for determining the proper number of components. More recently, a theoretical framework suggested that there is an ideal number of component classifiers for an ensemble such that having more or less than this number of classifiers would deteriorate the accuracy. It is called "the law of diminishing returns in ensemble construction." Their theoretical framework shows that using the same number of independent component classifiers as class labels gives the highest accuracy. == Common types of ensembles == === Bayes optimal classifier === The Bayes optimal classifier is a classification technique. It is an ensemble of all the hypotheses in the hypothesis space. On average, no other ensemble can outperform it. The Naive Bayes classifier is a version of this that assumes that the data is conditionally independent on the class and makes the computation more feasible. Each hypothesis is given a vote proportional to the likelihood that the training dataset would be sampled from a system if that hypothesis were true. To facilitate training data of finite size, the vote of each hypothesis is also multiplied by the prior probability of that hypothesis. The Bayes optimal classifier can be expressed with the following equation: y = a r g m a x c j ∈ C ∑ h i ∈ H P ( c j | h i ) P ( T | h i ) P ( h i ) {\displaystyle y={\underset {c_{j}\in C}{\mathrm {argmax} }}\sum _{h_{i}\in H}{P(c_{j}|h_{i})P(T|h_{i})P(h_{i})}} where y {\displaystyle y} is the predicted class, C {\displaystyle C} is the set of all possible classes, H {\displaystyle H} is the hypothesis space, P {\displaystyle P} refers to a probability, and T {\displaystyle T} is the training data. As an ensemble, the Bayes optimal classifier represents a hypothesis that is not necessarily in H {\displaystyle H} . The hypothesis represented by the Bayes optimal classifier, however, is the optimal hypothesis in ensemble space (the space of all possible ensembles consisting only of hypotheses in H {\displaystyle H} ). This formula can be restated using Bayes' theorem, which says that the posterior is proportional to the likelihood times the prior: P ( h i | T ) ∝ P ( T | h i ) P ( h i ) {\displaystyle P(h_{i}|T)\propto P(T|h_{i})P(h_{i})} hence, y = a r g m a x c j ∈ C ∑ h i ∈ H P ( c j | h i ) P ( h i | T ) {\displaystyle y={\underset {c_{j}\in C}{\mathrm {argmax} }}\sum _{h_{i}\in H}{P(c_{j}|h_{i})P(h_{i}|T)}} === Bootstrap aggregating (bagging) === Bootstrap aggregation (bagging) involves training an ensemble on bootstrapped data sets. A bootstrapped set is cr

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